If j > 1, is integer j a prime number? (1) When j is div

Expert replies

varun289: Master | Next Rank: 500 Posts; Posts: 298; Joined: Sun Jun 03, 2012 6:42 amFollowed by: 7 members; Location: New delhi; Thanked: 10 times; GMAT Score:590

by varun289 » Mon Apr 29, 2013 10:16 pm

If j > 1, is integer j a prime number?

(1) When j is divided by 3, the remainder is 1.

(2) When j is divided by 2, the remainder is 1.

Like this post

Source: Beat The GMAT — Problem Solving | Mon Apr 29, 2013 10:16 pm

GMAT/MBA Expert

Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Mon Apr 29, 2013 10:26 pm

varun289 wrote:If j > 1, is integer j a prime number?

(1) When j is divided by 3, the remainder is 1.
(2) When j is divided by 2, the remainder is 1.

One simple thing about prime number is they are rarely predictable and there is no formula to generate a prime number. A prime number may be represented in a particular form but that particular form will not always generate prime numbers.

So, whenever you come across this type of problem, combine both statements together and try to find contradiction. In fact, with practice you'll happen to know that answer to this particular problem is definitely E. Find a contradiction just to be more confident.

Here, if we combine both statements, it simply means when j is divided by 6 it leaves a remainder of 1. So, j is one more than a multiple of 6.

7 = 6*1 + 1 ---> 7 is prime
25 = 6*4 + 1 ---> 25 is not prime

We have our contradiction.
So, both statements together is also not sufficient.

The correct answer is E.

Go through this discussion made by Anurag on a problem testing the same concept (please scroll down and read his follow-on posts also) >> https://www.beatthegmat.com/num-prp-t74492.html#335738

Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

Â§ GMAT with Gurome Â§ Admissions with Gurome Â§ Career Advising with Gurome Â§

Like this post

killerdrummer: Senior | Next Rank: 100 Posts; Posts: 89; Joined: Wed Mar 13, 2013 3:36 amFollowed by: 1 member; Thanked: 10 times

by killerdrummer » Mon Apr 29, 2013 11:10 pm

(1) When j is divided by 3, the remainder is 1.

N =3K +1

Nature of this number -> either odd or even and as we know except 2, all primes are odd .
So this option alone is not sufficient

e.g. 7,10

Insufficient.

(2) When j is divided by 2, the remainder is 1.

N= 2K+1

Nature of this number -> Odd
11 is odd and prime, but 15 is odd and not prime.

e.g. 5,9

Insufficient.

Combining 1 and 2

Nature of this number : 6K +1

Anju has explained this part already !

Like this post

Blue_Skies: Senior | Next Rank: 100 Posts; Posts: 81; Joined: Thu May 03, 2012 1:48 pm; Thanked: 4 times

by Blue_Skies » Tue May 07, 2013 6:39 pm

Answer is E.

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue May 07, 2013 6:58 pm

varun289 wrote:If j > 1, is integer j a prime number?

(1) When j is divided by 3, the remainder is 1.

(2) When j is divided by 2, the remainder is 1.

When it comes to remainders, we have a nice rule that says:

If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.

For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

Okay, now onto the question.

Target question: Is integer j a prime number?

Statement 1: When j is divided by 3, the remainder is 1.
Possible values of j: 4, 7, 10, 13, 16, 19, 22, 25...
As you can see, some values of j are prime and some are not.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: When j is divided by 2, the remainder is 1.
Possible values of j: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, ...
As you can see, some values of j are prime and some are not.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
From statement 1: j could equal 4, 7, 10, 13, 16, 19, 22, 25...
From statement 2: j could equal 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, ...

Some numbers that satisfy both statements are 7, 13, 19, 25, . . .
Once again, some values of j are prime and some are not.
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review